Mathematical transformations of recurrent relations for different types of homologues

• Published in: Journal of chemometrics 2016-04, Vol.30 (4), p.217-225
• Main Author: Zenkevich, Igor G.
• Format: Article
• Language: English
• Subjects: Algorithms; Approximation; chemical applications; Chemometrics; Fragments; Homology; Mathematical analysis; mathematical transformations; Organic chemistry; Organic compounds; physicochemical properties; recurrent relations; sub-types of homology; Topology; Transformations (mathematics)
• ISSN: 0886-9383; 1099-128X
• DOI: 10.1002/cem.2796

Most of discrete properties A of individual organic compounds belonging to single‐row homologous series (RX → RCH2X → … → R(CH2)nX) or multi‐row series (RkY → [RCH2]kY → … [R(CH2)n]kY, k > 1) can be approximated with first order linear recurrent relations A(n + 1) = aA(n) + b. The important chemical property of recurrences is the equality of coefficients a and b for various homologous series of similar topology (with the same homologous differences at the constancy of the number of rows). The values of coefficients a and b for single‐ and multi‐rows series even with the same structural fragments X = Y are different. The algorithm of the mutual recalculating of the coefficients of recurrent relations for single‐ and multi‐rows homologous series is proposed and considered. It allows evaluating different physicochemical properties of insufficiently characterized unsymmetrical organic compounds with different alkyl substituents, like C2H5NHC3H7, (CH3)2B(C2H5), (CF3)N(C2F5)2, etc., using the data for better characterized “symmetrical” homologues (illustrated by examples). Copyright © 2016 John Wiley & Sons, Ltd. Most of discrete properties A of individual organic compounds belonging to single‐row homologous series (RX → RCH2X → … → R(CH2)nX) or multi‐row series (RkY → [RCH2]kY → … [R(CH2)n]kY, k > 1) can be approximated with first order linear recurrent relations A(n + 1) = aA(n) + b. The values of coefficients a and b for single‐ and multi‐rows series even with the same structural fragments X = Y are different. The algorithm of the mutual recalculating of the coefficients of recurrent relations for single‐ and multi‐rows homologous series is proposed and considered. It allows evaluating different physicochemical properties of insufficiently characterized unsymmetrical organic compounds with different alkyl substituents, like C2H5NHC3H7, (CH3)2B(C2H5), (CF3)N(C2F5)2, etc., using the data for better characterized “symmetrical” homologues (illustrated by examples).